Error detection without post-selection in adaptive quantum circuits

TL;DR

This work uses Quantinuum's H2 quantum computer to perform logical simulations of a non-equilibrium phase transition using the [[4,2,2]] code, and shows how simulations of open quantum systems can benefit from error detection.

Abstract

Current quantum computers are limited by errors, but have not yet achieved the scale required to benefit from active error correction in large computations. We show how simulations of open quantum systems can benefit from error detection. In particular, we use Quantinuum's H2 quantum computer to perform logical simulations of a non-equilibrium phase transition using the [[4,2,2]] code. Importantly, by converting detected errors into random resets, which are an intended part of the dissipative quantum dynamics being studied, we avoid any post-selection in our simulations, thereby eliminating the exponential cost typically associated with error detection. The encoded simulations perform near break-even with unencoded simulations at short times.

Figures (4)

• Figure 1: How error detection can be used to remove errors without post-selection in a quantum circuit with random resets (e.g., to a mixed state $\rho$). (Left) In the physical circuit, resets (orange) are randomly inserted and hardware errors (blue) occur randomly, spreading and corrupting the circuit's output. (Right) In the logical circuit encoded into an error detection code, hardware errors can be detected and converted into resets, preventing the spread of errors without needing to discard the circuit realization. Note that the probability of a reset is now increased by the detection events, so the injected resets rate needs to be decreased to compensate.
• Figure 2: a The dissipative quantum circuit studied in this work, encoded into multiple [[4,2,2]] quantum error detection code blocks. Each qubit shown is a logical qubit and gates are logical gates (the encoding using physical qubits is not shown here). The two-qubit gates are controlled-$R_x(\theta)$ rotation gates. The orange boxes are random two-qubit resets that occur with probability $p$. b The [[4,2,2]] code's logical Pauli operators $\bar{Z}_{1/2},\bar{X}_{1/2}$ and stabilizers $S_{Z/X}$. c The two competing processes in the circuit acting on computational basis states, a branching process that spreads $|1\rangle$ states to other qubits (controlled by $\theta$) and a decay process that causes $|1\rangle$ states to decay to $|0\rangle$ states (at a rate controlled by $p$). d Using an error detection code, the circuit can be made adaptive so that random resets are intentionally injected at random or are triggered by a leakage detection (LD) or error detection (QED) event generated by quantum hardware noise.
• Figure 3: a The active site density profile $\langle n(r,t)\rangle$ obtained from the logical circuit run on H2 compared with the exact profile computed from classical numerics (reflected about $r=0$). b The two-qubit (2Q) gate and qubit overheads of the logical circuits with and without qubit-reuse. c The experimental results obtained on H2. The total number of active sites on the right half of the system versus time, comparing physical (purple diamonds) and logical results (red circles) against classical exact numerics (solid lines). d The relative error of the observable in c from the exact result for the logical and physical circuits.
• Figure 4: a The space-time record of error detection events and injected resets for one shot of a $t=7, p=0.2$ circuit run on H2. b The average space-time probabilities of detecting an error in the calibration run. c The average space-time probabilities of resetting a code block in the main run, which includes injected resets as well as detected resets. d The average space-time probabilities of resetting a code block after using the reweighting scheme.